A078653 a(n) = prime(k) where k = n-th prime congruent to 1 mod 4.

11, 41, 59, 109, 157, 179, 241, 283, 367, 461, 509, 547, 599, 617, 773, 859, 919, 1031, 1087, 1171, 1201, 1447, 1471, 1523, 1621, 1723, 1787, 1823, 1913, 2081, 2099, 2269, 2351, 2381, 2549, 2683, 2719

Offset

1,1

Comments

Sum 1/a(n) appears to converge albeit slowly.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = A000040(A002144(n)). [Bruno Berselli, Aug 14 2012]

Mathematica

With[{pc14=Select[Prime[Range[100]], Mod[#, 4]==1&]}, Flatten[Table[ Prime[ Take[ pc14, {n}]], {n, 40}]]] (* Harvey P. Dale, Aug 12 2011 *)

Prog

(PARI) pip(n, m, r) = {sr=0; forprime(x=3, n, if(x%m == r, v=prime(x); sr+=1.0/v; print1(v" "); ) ); print(); print("m="m" r="r" sr="sr); }
(Magma) [NthPrime(n): n in PrimesUpTo(400) | n mod 4 eq 1]; // Bruno Berselli, Aug 14 2012

Crossrefs

Cf. A006450, A078654.

Sequence in context: A350006 A122015 A192820 * A040167 A040170 A333085

Adjacent sequences: A078650 A078651 A078652 * A078654 A078655 A078656

Keyword

nonn,easy

Author

Cino Hilliard, Dec 14 2002

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Aug 14 2012

Status

approved